Synthetic Division Calculator

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Use synthetic division for:

2x3 - 4x2 - 22x + 24
x - 1

Determine our root divisor:

Solve the divisor equation x - 1 = 0
Add 1 to each side of the equation to get
x - 1 + 1 = 0 + 1
Therefore, our root becomes x = 1

	2	-4	-22	24
1

	2	-4	-22	24
1	↓
	2

Multiply our root 1 by 2
Take 2 and put that in column 2:

	2	-4	-22	24
1		2
	2

2 + -4 = -2
Put this in the answer column 2:

	2	-4	-22	24
1		2
	2	-2

Multiply our root 1 by -2
Take -2 and put that in column 3:

	2	-4	-22	24
1		2	-2
	2	-2

-2 + -22 = -24
Put this in the answer column 3:

	2	-4	-22	24
1		2	-2
	2	-2	-24

Multiply our root 1 by -24
Take -24 and put that in column 4:

	2	-4	-22	24
1		2	-2	-24
	2	-2	-24

-24 + 24 = 0
Put this in the answer column 4:

	2	-4	-22	24
1		2	-2	-24
	2	-2	-24	0

Leading Answer Term = x(3 - 1) = x2

Since the last number in our result line = 0, we will not have a remainder and have a clean quotient which is shown below in our answer:

Answer = 2x2 - 2x - 24

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It appears your answer forms a quadratic equation since the maximum power of your result equation is 2 and your remainder is zero. Click here to solve this quadratic equation

How does the Synthetic Division Calculator work?

Free Synthetic Division Calculator - Using Ruffinis Rule, this performs synthetic division by dividing a polynomial with a maximum degree of 6 by a term (x ± c) where c is a constant root using the factor theorem. The calculator returns a quotient answer that includes a remainder if applicable. Also known as the Rational Zero Theorem
This calculator has 1 input.

What 3 formulas are used for the Synthetic Division Calculator?

For x + a, our root is -1 * a
Write down our coefficients horizontally and our root of a to the left
Multiply root by last result and repeat process

For more math formulas, check out our Formula Dossier

What 4 concepts are covered in the Synthetic Division Calculator?

divisionseparate a number into partspolynomialan expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).ruffinis rulean efficient method of dividing a polynomial by a linear factor, with or without a remainder. synthetic divisiona shorthand method for dividing a polynomial by a linear factor

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